RIYADH, Saudi Arabia — Secretary of State John Kerry on Thursday sought to reassure Saudi Arabia and other Gulf states that the negotiation of a nuclear accord with Iran would not lead the Obama administration to let down its guard against any Iranian interference in the region.

With the Saudi foreign minister by his side, Mr. Kerry said at a news conference here that the administration was committed to standing up to Iran’s “intervention.”

“We are not seeking a grand bargain,” Mr. Kerry said, offering the assurance that the administration was not pursuing a broader rapprochement with Iran that could come at the expense of its Arab rivals. “We will not take our eye off of Iran’s other destabilizing actions.”

But it was clear from the remarks of the Saudi foreign minister, Prince Saud al-Faisal, that Arab nations are acutely worried about Iran’s effort to exercise influence in the region and the prospect that it could grow as economic sanctions are lifted as part of a nuclear deal.

Prince Saud cited reports of Iran’s role in supporting the Iraqi operation to retake Tikrit as an indication of what he called Tehran’s “hegemonic” tendencies.

“Tikrit is a prime example of what we are talking about,” he said. Decisions about war and peace, he said, were no longer solely being made by the Iraqi government but were “in the hands of Iran.”

One day after completing a round of negotiations with his Iranian counterpart, Mohammad Javad Zarif, Mr. Kerry met for an hour Thursday with King Salman at the Diriya Farm outside Riyadh.

He also met at the Riyadh Air Base on Thursday morning with the foreign ministers from the Gulf Cooperation Council, which is made up of Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates.

A broad concern for Arab states is that lifting economic sanctions against Tehran — the quid pro quo for the nuclear limits Iran is being asked to accept — will not only help Iran’s economy but also enhance its ability to send weapons and Quds paramilitary forces to support President Bashar al-Assad in Syria.

Arab nations are also worried about Iran’s support for Houthi rebels in Yemen and its longtime support for Hezbollah, the Lebanese militant group.

Seeking to ease those concerns, Mr. Kerry said that he would convene a meeting in Washington with senior officials from the Gulf states to discuss future security arrangements in the region.

He also sought to play down the reports of Iranian aid in the Tikrit operation. Mr. Kerry insisted that the offensive had been planned by Iraqi government, that Iran’s involvement in Iraq was not coordinated with the United States and that the role of the militias Iran was backing would fade as the American effort to rebuild the Iraqi army gathered steam.

Before flying to Saudi Arabia early Thursday, Mr. Kerry held three days of talks in Montreux, Switzerland, with Mr. Zarif, the Iranian foreign minister, which American officials said yielded some progress.

A senior State Department official said the goal now was to work out an “understanding” by the end of March on what a detailed agreement to limit Iran’s program would look like that.

Toward that end, Mr. Kerry plans to meet with Mr. Zarif on March 15, probably in Geneva. Intensive consultations are planned before then, including a meeting on Saturday on Paris Mr. Kerry is holding with the foreign ministers of Britain, France and Germany.